Yield curve fitting table

The different behaviour between the two vapours is even more evident if we fit the entire experimental curve directly with Equation (4.6) after expansion into 10 terms (n = 1, 2, 3,. .. 10). The DCM curve yields a nearly perfect fit (Figure 4.8, bottom), indicating that the DCM transport can be described well by the simple Fickian diffusion with a single diffusion constant, independent of time or concentration. In this case the values of D and S are directly obtained from the curve fit and they agree within an error of a few percent with the values in Table 4.3, obtained by the tangent method. 

The data were analyzed in Rgure AIO.2.2 according to the four-element model. First, at zero time, the strain yields Fj. The straight-line portion at long times, separated as curve 1, yields Then, by subtraction, curve 2 was obtained. By simple curve fittings E2, r 2, and T2 can be determined. The retardation time for Veiveeta cheese was found to be about 7 to 9 minutes (see Table AIO.2.1). 

Figure 3. Fitting the C4 region of a CP/MAS C-NMR spectrum recorded on cellulose / isolatedfrom cotton linters by HCl(aq) hydrolysis (2.5MHCl(aq) 100 C 17h, yield about 80 %. After hydrolysis the cellulose is a colloidal sol). The experimental spectrum is shown as a broken line. The fttted spectral lines and their superposition are shown as solid lines. The broken line of the experimental spectrum is partialfy hidden by the superimposedfttted curves. See Table I for...

For both curves, fitting yields very close values of the exchange current density of k — 10 A cm (Table 5.5). This value of i is nearly two orders of magnitude less than the one obtained in Dobson et al. (2012) from the same set of curves using a flooded agglomerate model. Note that, as discussed in Dobson et al. (2012), their value is an order of magnitude higher than expected thus, the values of i indicated in Table 5.5 could be closer to reality. 

X is an acidity function based on the first-order approximation, Eq. (8-92). Values of X have been assigned by an iterative procedure. The data consist of values of Cb/cbh+ as functions of Ch+ for a large number of indicators. For each indicator an initial estimate of pXbh+ and m is made and X is calculated with Eq. (8-94). This yields a large body of X values, which are fitted to a polynomial in acid concentration. From this fitted curve smoothed X values are obtained, and Eq. (8-94), a linear function in X. allows refined values of pXbh + and m to be obtained. This procedure continues until the parameters undergo no further change. Table 8-20 gives X values for sulfuric and perchloric acid solutions. ... 

This value is identified in F tables for the corresponding dfc and dfs. For example, for the data in Figure 11.13, F = 7.26 for df=6, 10. To be significant at the 95% level of confidence (5% chance that this F actually is not significant), the value of F for df = 6, 10 needs to be > 4.06. In this case, since F is greater than this value there is statistical validation for usage of the most complex model. The data should then be fit to a four-parameter logistic function to yield a dose-response curve. 

As shown by the dashed curves in Figure 30.16, fitting 1.0 Hz results with Equation 30.4 yields plateau values, which likely have no physical meaning, with respect to 0.5 Hz data. However, fit parameters of this equation (as given in Table 30.2) allow the slope to be calculated at any strain within the experimental window. It follows that the slope at a given strain, for instance 200%,... 

Figure 4.51. Distribution of experimental data. Six experimental formulations (strengths 1, 2, resp. 3 for formulations A, respectively B) were tested for cumulative release at five sampling times (10, 20, 30, 45, respectively 60 min.). Twelve tablets of each formulation were tested, for a total of 347 measurements (13 data points were lost to equipment malfunction and handling errors). The group means were normalized to 100% and the distribution of all points was calculated (bin width 0.5%, her depicted as a trace). The central portion is well represented by a combination of two Gaussian distributions centered on = 100, one that represents the majority of points, see Fig. 4.52, and another that is essentially due to the 10-minute data for formulation B. The data point marked with an arrow and the asymmetry must be ignored if a reasonable model is to be fit. There is room for some variation of the coefficients, as is demonstrated by the two representative curves (gray coefficients in parentheses, h = peak height, s = SD), that all yield very similar GOF-figures. (See Table 3.4.)...

These factors are used in the equations given in Table I. The computation requires only that the variance ratios be accurately known. The absolute precision of the method may change from day to day without affecting the validity of either the least-squares curve-of-best fit procedure or the confidence band calculations. (It is not practical to regularly monitor local variances, and errors may develop in variance ratios. Eowever, the error due to incorrect ratios will almost always be much less than the error due to assuming constant variance. Even guessed values of, say, S a concentration are likely to yield more precise data.)... 

In analytical spectrometry there are many types of calibration curves which are set up by measuring spectrometric reference solutions. The measurements yield a curve of absorbance versus concentration, and the points between the data of the reference solutions are interpolated by fitting a suitable curve, which normally follows the Beer-Lambert law and which gives rise to a straight line through the origin of the coordinate system. The measurement conditions and the results of the calibration curve evaluations in the case of chromium and lead measurements by electrothermal atomic absorption spectrometry are presented in Table 1. 

Since the use of equilibrium (Freundlich) type with n > 1 is uncommon, we also attempted the kinetic reversible approach given by equation 12.2 to describe the effluent results from the Bs-I column. The use of equation 12.2 alone represents a fully reversible S04 sorption of the n-th order reaction where kj to k2 are the associated rates coefficients (Ir1). Again, a linear form of the kinetic equation is derived if m = 1. As shown in Figure 12.7, we obtained a good fit of the Bs-I effluent data for the linear kinetic curve with r2 = 0.967. The values of the reaction coefficients kj to k2, which provided the best fit of the effluent data, were 3.42 and 1.43 h with standard errors of 0.328 and 0.339 h 1, respectively (see Table 12.3). Efforts to achieve improved predictions using nonlinear (m different from 1) kinetics was not successful (figures not shown). We also attempted to incorporate irreversible (or slowly reversible) reaction as a sink term (see equation 12.5) concurrently with first-order kinetics. A value of kIIT = 0.0456 h 1 was our best estimate, which did not yield improved predictions of the effluent results as shown in Figure 12.7. 

How well do the sedimentation coefficients and densities predicted by the model match the values actually observed for LDL Excellent agreement with the experimental points is shown by the solid curve of Fig. 2, which is a plot of the values for 525,1.20 given in Table II. However, this agreement was achieved by selecting a value for the partial specific volume of the cholesteryl esters to make the best fit, yielding the value of 1.058 ml/g for this this quantity. [If a value of 1.044 ml/g were employed for the partial specific volume of the cholesteryl esters, as was used by Sata et al. (1972), the values of 525,1.20 listed in Table II would have decreased by about 3,5%. The values of S[ in Table II would have dropped by 1 to 2 Svedbergs.]... 

In order to test the applicability of the model over a wider range of conditions the kinetics derived at 10 C/tnin from Table 1) was used to predict the pyrolysis of wheat straw heated to 300 C at 10°C/min, then kept isothermal for 60 min, before heating to bOO C at 10°C/min, see Fig. 3. The experimental data show that the addition of a 60 min hold time at 300°C results in somewhat different mass loss curve. The initial mass loss follows that of the data heated directly to 600 C, but when 300 C is reached, the mass loss rate becomes much lower, and after 60 min at 300 C, the conversion is only about 0.8. Full conversion is reached when the temperature is raised to 600 C. The char yield for the two experiments was approximately the same. The model, which fit the direct heating to 600°C reasonably well, does not work for the case with a 60 min isothermal segment at 300°C is inserted. The model predicted that the pyrolysis was far too fast, and a full conversion is predicted under the isothermal segment. This shows that first order kinetics only works well on the data on which it was fitted. A single first order model cannot predict the pyrolysis behavior under different conditions. 

Figure 31. Representative data showing OH formation following 236 nm CO2-HI excitation. The ordinates in (a) and (b) are the Qi,(l) and Qi,(6) LIF signals, respectively, while the abscissa is the delay time. The dashed curve is the response function of the laser system. The solid curves are the calculated best fits, assuming a two-parameter description for the time dependence of OH formation the best least-squares fits yielded (a) t, = 0.9 ps and Tj = 1.9 ps, and (b) x, = 0.7 ps and Xj = 1.1 ps (see Table 4). The points at the top are the residuals between the experimental points and the smooth fit. From Ref. 43 with permission of the Journal of Chemical Physics.

---